Finite Group Databasebeta

← #20246678

Subgroups — #20246678

Order 6016.

504 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 167 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×Dic47C211yesmaximal, characteristic
2C2×#13093989C211yesmaximal, characteristic
3#15689056C212yesmaximal
4#15689055C211yesmaximal, characteristic
5#15689053C211yesmaximal, characteristic
6#15689044C212yesmaximal
7#15689042C211yesmaximal, characteristic
8C4⋊C4×Dic47C212yesmaximal
9#15688974C212yesmaximal
10#15688968C211yesmaximal, characteristic
11C47×#395C211yesmaximal, characteristic
12C22×Dic94C2211yescharacteristic
13Q8×Dic47—24no—
14#13093989—24no—
15C2×C4⋊Dic47C2212yes—
16C2×C4⋊Dic47C2212yes—
17C2×C4⋊Dic47C2211yescharacteristic
18C2×Dic47⋊C4C2212yes—
19C2×Dic47⋊C4C2212yes—
20C2×Dic47⋊C4C2211yescharacteristic
21C2×Dic47⋊C4C2211yescharacteristic
22C2×C4×Dic47C2211yescharacteristic
23C2×C4×Dic47C2212yes—
24C2×C4×Dic47C2211yescharacteristic
25C2×C4×Dic47C2211yescharacteristic
26C2×C4×Dic47C2212yes—
27C47⋊#95C2211yescharacteristic
28C47⋊#95C2212yes—
29C47⋊#95C2212yes—
30C47⋊#95C2212yes—
31C47⋊#95C2212yes—
32C22×Q8×C47C2211yescharacteristic
33C2×C4⋊C4×C47C2212yes—
34C2×C4⋊C4×C47C2211yescharacteristic
35#95×C47C2211yescharacteristic
36#95×C47C2212yes—
37C2×Q8×C47—22no—
38C2×Q8×C47—24no—
39C22×C4×C47C2311yescharacteristic
40C22×C4×C47C2311yescharacteristic
41C22×C4×C47C2312yes—
42C22×C4×C47C2312yes—
43C22×C4×C47C2311yescharacteristic
44C22×Dic47C2311yescharacteristic
45C22×Dic47C2312yes—
46C22×Dic47C2311yescharacteristic
47C22×Dic47C2312yes—
48C22×Dic47C2311yescharacteristic
49C22×Dic47C2311yescharacteristic
50C2×Dic94—22no—
51C2×Dic94—22no—
52C2×Dic94—22no—
53C4⋊C4×C47—22no—
54C4⋊C4×C47—24no—
55C4⋊Dic47—22no—
56C4⋊Dic47—24no—
57C4⋊Dic47—24no—
58Dic47⋊C4—22no—
59Dic47⋊C4—24no—
60Dic47⋊C4—24no—
61Dic47⋊C4—22no—
62C4×Dic47—22no—
63C4×Dic47—22no—
64C4×Dic47—24no—
65C4×Dic47D414yes—
66C4×Dic47Q818yescomplemented
67C23×C47C2411yescharacteristic
68Q8×C47—28no—
69C2×C4×C47—22no—
70C2×C4×C47—21no—
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47—21no—
74C2×C4×C47—22no—
75C2×C4×C47—22no—
76C2×C4×C47—21no—
77C2×C4×C47—22no—
78C2×C4×C47C2×D412yes—
79C2×C4×C47C2×Q814yes—
80C2×C4×C47#4114yes—
81C2×C4×C47#4112yes—
82C2×Dic47—21no—
83C2×Dic47—22no—
84C2×Dic47—22no—
85C2×Dic47—21no—
86C2×Dic47—21no—
87C2×Dic47—21no—
88C2×Dic47—21no—
89C2×Dic47—22no—
90C2×Dic47—22no—
91C2×Dic47—22no—
92C2×Dic47—22no—
93C2×Dic47C2×D412yes—
94C2×Dic47C2×D412yes—
95C2×Dic47C2×Q814yes—
96C2×Dic47C2×Q814yes—
97C2×Dic47#4112yes—
98Dic94—28no—
99C22×C47C22×D411yescharacteristic
100C22×C47C22×Q812yes—
101C22×C47C2×#4111yescharacteristic
102C22×C47C2×#4112yes—
103C22×C47C2×#4111yescharacteristic
104C4×C47—22no—
105C4×C47—22no—
106C4×C47—24no—
107C4×C47—24no—
108C4×C47—41no—
109Dic47—22no—
110Dic47—22no—
111Dic47—24no—
112Dic47—41no—
113Dic47—42no—
114Dic47C4⋊Q814yes—
115#2399—471nomaximal, Sylow
116C2×C47#52511yescharacteristic
117C2×C47#52511yescharacteristic
118C2×C47C2×C4⋊Q811yescharacteristic
119C2×C47#53312yes—
120C2×C47#53312yes—
121C2×C4×Q8—471no—
122C2×C4×Q8—471no—
123#398—471no—
124#398—472no—
125#398—471no—
126#395—471no—
127#395—472no—
128#395D4711yescharacteristic
129C4×C4⋊C4—472no—
130C4×C4⋊C4—472no—
131#376—471no—
132C47#239911yescharacteristic, complemented, Sylow
133C22×Q8—471no—
134C22×Q8C2×D4711yescharacteristic
135C4×Q8—944no—
136C4×Q8—944no—
137C2×C4⋊C4—471no—
138C2×C4⋊C4—471no—
139C2×C4⋊C4—472no—
140C2×C4⋊C4—471no—
141C2×C4⋊C4—472no—
142C2×C4⋊C4—472no—
143C2×C4⋊C4—472no—
144C2×C4⋊C4C2×D4711yescharacteristic
145C2×C4⋊C4C2×D4712yes—
146C2×C42—471no—
147C2×C42—472no—
148C2×C42—471no—
149C2×C42—472no—
150C2×C42—471no—
151#95—471no—
152#95—472no—
153#95—472no—
154#95—472no—
155#95—472no—
156#95C2×D4711yescharacteristic
157#95C2×D4712yes—
158C2×Q8—22no—
159C2×Q8—24no—
160C2×Q8—942no—
161C2×Q8—942no—
162C2×Q8—942no—
163C22×C4—471no—
164C22×C4—472no—
165C22×C4—471no—
166C22×C4—471no—
167C22×C4—472no—
168C22×C4—471no—
169C22×C4C22×D4711yescharacteristic
170C22×C4C22×D4711yescharacteristic
171C22×C4C22×D4712yes—
172C22×C4C22×D4712yes—
173C22×C4C22×D4711yescharacteristic
174C4⋊C4—22no—
175C4⋊C4—24no—
176C4⋊C4—942no—
177C4⋊C4—944no—
178C4⋊C4—944no—
179C4⋊C4—942no—
180C4⋊C4—942no—
181C4⋊C4—944no—
182C4⋊C4—944no—
183C42—474no—
184C42—478no—
185C42—942no—
186C42—944no—
187C42—942no—
188C23C23×D4711yescharacteristic
189Q8—28no—
190Q8—948no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—472no—
201C2×C4—474no—
202C2×C4—472no—
203C2×C4—474no—
204C2×C4—472no—
205C2×C4—941no—
206C2×C4—941no—
207C2×C4—942no—
208C2×C4—942no—
209C2×C4—941no—
210C2×C4—941no—
211C2×C4—941no—
212C2×C4—942no—
213C2×C4—942no—
214C2×C4—942no—
215C2×C4—942no—
216C2×C4D4×D4712yes—
217C2×C4#1062535214yes—
218C2×C4Q8×D4714yes—
219C2×C4#1062535412yes—
220C22C2×D4×D4711yescharacteristic
221C22C2×Q8×D4712yes—
222C22#41×D4711yescharacteristic
223C22C2×#1062535212yes—
224C22C2×#1062535411yescharacteristic
225C4—22no—
226C4—24no—
227C4—22no—
228C4—24no—
229C4—41no—
230C4—474no—
231C4—942no—
232C4—942no—
233C4—944no—
234C4—1881no—
235C4—1882no—
236C2#1568962911yescharacteristic
237C2#1568963611yescharacteristic
238C2C4⋊Q8×D4711yescharacteristic
239C2#1568967512yes—
240C2#1568967812yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#395C2
hypercenter#395D47
hypocenterC47#2399
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #395

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
66. C4×Dic47Q8semidirect
132. C47#2399semidirect